By Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi, Laurence A. Wolsey

In 1958, Ralph E. Gomory reworked the sphere of integer programming whilst he released a paper that defined a cutting-plane set of rules for natural integer courses and introduced that the tactic may be sophisticated to provide a finite set of rules for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a distinct workshop celebrating fifty years of integer programming used to be held in Aussois, France, as a part of the twelfth Combinatorial Optimization Workshop. It includes reprints of key historic articles and written models of survey lectures on six of the most well liked subject matters within the box by means of wonderful participants of the integer programming group. invaluable for somebody in arithmetic, computing device technology and operations learn, this e-book exposes mathematical optimization, in particular integer programming and combinatorial optimization, to a vast viewers.

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Kuhn 2 The Hungarian Method for the Assignment Problem 41 42 Harold W. Kuhn 2 The Hungarian Method for the Assignment Problem 43 44 Harold W. Kuhn 2 The Hungarian Method for the Assignment Problem 45 46 Harold W. Kuhn 2 The Hungarian Method for the Assignment Problem 47 Chapter 3 Integral Boundary Points of Convex Polyhedra Alan J. Hoffman and Joseph B. Kruskal Introduction by Alan J. Hoffman and Joseph B. Kruskal Here is the story of how this paper was written. (a) Independently, Alan and Joe discovered this easy theorem: if the “right hand side” consists of integers, and if the matrix is “totally unimodular”, then the vertices of the polyhedron defined by the linear inequalities will all be integral.

G. Rinnooy Kan, and A. ), North Holland, Amsterdam, 1991, pp. 77–81. 2. A. Schrijver, Combinatorial optimization: polyhedra and efficiency, Vol. A. Paths, Flows, Matchings, Springer, Berlin, 2003. 2 The Hungarian Method for the Assignment Problem 31 32 Harold W. W. Kuhn, The Hungarian Method for the Assignment Problem, Naval Research Logistics Quarterly 2 (1955) 83–97. 2 The Hungarian Method for the Assignment Problem 33 34 Harold W. Kuhn 2 The Hungarian Method for the Assignment Problem 35 36 Harold W.

Fulkerson, and Selmer M. Johnson 1 Solution of a Large-Scale Traveling-Salesman Problem 27 28 George B. Dantzig, Delbert R. Fulkerson, and Selmer M. Johnson Chapter 2 The Hungarian Method for the Assignment Problem Harold W. Kuhn Introduction by Harold W. Kuhn This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin. A. campus.